Unification of Gravity and Standard Model: Weyl-Dirac-Born-Infeld action

Abstract: We construct a unified (quantum) description by the gauge principle of gravity and Standard Model (SM), that extends the Dirac-Born-Infeld action to the SM and Weyl geometry in $d$ dimensions, hereafter called Weyl-Dirac-Born-Infeld action (WDBI). This action is a general gauge theory of SM and Weyl group (of dilatations and Poincar\'e symmetry), in the Weyl gauge covariant (metric) formulation of Weyl geometry. The theory is SM and Weyl gauge invariant in arbitrary $d$ dimensions, hence there is no Weyl anomaly. The action has the unique elegant feature, not present in other gauge theories or even in string theory, that it is mathematically well-defined in $d$ dimensions, with no need to introduce a UV regulator (scale or field). The WDBI action actually {\it predicts} that gravity, through (Weyl covariant) space-time curvature, acts as UV regulator of both SM and gravity in $d=4$. A series expansion of the WDBI action (in dimensionless couplings) recovers in the leading order the Weyl gauge invariant action of SM and Weyl (gauge theory of) quadratic gravity. The SM and Einstein-Hilbert gravity are recovered in the Stueckelberg broken phase of Weyl gauge symmetry, which also restores Riemannian geometry below Planck scale. Sub-leading orders are suppressed by powers of (dimensionless) gravitational coupling ($\xi$) of Weyl quadratic gravity.